Abstract
The Multiple Knapsack Problem (MKP) (with equal capacities) can be defined as follows: Given a set of n items with positive integer weights and profits, a subset has to be selected such that the items in this subset can be packed into m knapsacks of equal capacities and such that the total profit of all items in the knapsacks is maximized. For m = 1 (MKP) reduces to the classical 0-1 single knapsack problem. It is known that (MKP) admits no fully polynomial-time approximation scheme even for m = 2 unless \(\mathcal{P} = \mathcal{NP}\). In this paper we present a polynomial time approximation scheme for (MKP) even if m is part of the input. This solves an important open problem in the field of knapsack problems.
Keywords
- Knapsack Problem
- Critical Item
- Polynomial Time Approximation Scheme
- Small Item
- Fully Polynomial Time Approximation Scheme
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References
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© 1999 Springer-Verlag Berlin Heidelberg
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Kellerer, H. (1999). A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds) Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 1999 1999. Lecture Notes in Computer Science, vol 1671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48413-4_6
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DOI: https://doi.org/10.1007/978-3-540-48413-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66329-4
Online ISBN: 978-3-540-48413-4
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